178 



NATURE 



[February 9, 192: 



Fig. I shows. It begins with many genera of one 

 species, fewer (but still many) of two, and tapers 

 away in a tail to the larger genera, the tail being 

 longer the larger the family or area dealt with (the 

 tails in the figufe are usually very incomplete : Com- 

 positae, for example, run to 1450). A number of 



Number of species 



10 20 30 40 50 



JL 



■6 -8 1-0 1-2 14 16 1-8 20 



log (N 9 of species) 



Fig. 2.— Log. curve for all flowering plants. 



curves are plotted together in Fig, i, and show that 

 this type of curve holds not only for all the genera 

 of the world, but also for all the individual families 

 both of plants and animals, for endemic and for non- 

 endemic genera, for local floras and faunas (as may 

 be verified in an hour), and even for very local 

 floras, such as that of Cambridge- 

 shire ; it holds even for Wicken , 

 Fen and other strictly local asso- 

 ciations of plants. It obtains, too, 

 as Mrs. Reid showed in a note 

 read the same evening, for all the 

 deposits of Tertiary fossils exam- 

 ined. For the first three numbers it 

 shows very clearly, but as the num- 

 bers become smaller they tend to be 

 irregular, though always diminish- 

 ing towards the end. If one take 

 only the tens, twenties, etc., one 

 obtains a practically smooth curve. 

 But now, if species of very 

 limited area and genera of one 

 species (which also have usually 

 small areas) are, with compara- 

 tively few exceptions, the young 

 beginners in the race of life, 

 and are descended in general from 

 the species of wider dispersal and 

 the larger genera, and if the number of species in a 

 genus is, broadly speaking, a measure of its age, the 

 idea at once suggests itself that a given stock may be 

 regarded as " throwing " generic variations much as 

 it throws offspring, so that the number of genera 

 descended from one prime ancestor may be expected 

 NO. 2728, VOL. 109] 



to increase in geometric ratio or according to 

 the law of compound interest. The number of 

 species descended from one ancestor might be 

 expected to follow the same form of law with 

 a more rapid rate of growth. On such a very 

 rough conception it is found that the form of fre- 

 quency distribution for sizes of 

 genera should follow the rule that 

 the logarithm of the number of 

 genera plotted to the logarithm of 

 the number of species gives a 

 straight line. Fig. 2 shows the 

 results of this method of plotting 

 for all the flowering plants of the 

 world. The dots give the data, 

 graduated ; some process of gradu- 

 ation had to be used, as the statis- 

 tics were based on the figures given 

 in the " Dictionary of the Flower- 

 ing Plants and Ferns," which are 

 rounded off in doubtful cases to 

 the nearest 5 or 10 (or greater 

 number in the large genera). It 

 will be seen that, up to genera of 

 some thirty or forty species, there 

 is an excellent fit to a straight line, 

 though there is a marked deficiency 

 of the larger genera — a point on 

 which further investigation is re- 

 quired. Single families show pre- 

 cisely the same rule, the lines not differing very 

 greatly in slope : Fig. 3 gives an illustration of the 

 chart for the Rubiaceae. Nor is the law one con- 

 fined to plant life, as is shown by Fig. 4, for the 

 family of Chrysomelidas amongst the beetles. 



It follows from the conception stated that the 

 N2 of species 



10 30 100 



24 



log (N9of species) 



Fig. 3. — Log. curve for Rubiaceae. 



excess of the slope of the line over unity should 

 measure the ratio of the rate of increase of genera 

 to that of species. The slope should always, there- 

 fore, lie between the limits i and 2, for a slope of 

 less than unity would have no meaning, and a slope 

 exceeding 2 would imply that generic variations 



